The present invention relates to a plant diagnostic system which diagnoses plants e.g., power generation plant etc.
In recent years, various plant diagnostic techniques have been studied with respect to plant processes such as the power generation process, and research and development related thereto are briskly conducted. As one of results of such research and development, there is a plant diagnostic system which has been already proposed by the inventors of the present invention and others (see Japanese Patent Application No. 58-102736).
According to this system, a plant to be diagnosed is expressed as an AR (Auto Regressive) model as shown in the following equation (1), and a residual .epsilon.(s) between an estimated value X(s) calculated based on this model and an actual plant value X(s) is calculated using the following equation (2). Then, whiteness of the residual .epsilon. thus obtained is qualified, thereby to recognize whether the plant is in and abnormal condition or not. ##EQU1## where X(s) is an estimated value of a plant value at a sampling time s, A is an AR coefficient matrix, X(s) is a plant value at the sampling time s and is expressed as ##EQU2## and M is degree of the AR model. EQU .epsilon.(s)=X(s)-X(s) (2)
where .epsilon.(s) is a residual at the sampling time s and is expressed as ##EQU3##
In the above-mentioned plant diagnostic system, a correlation function .phi..sub.ij used for qualification of whiteness of the residual was obtained using the following equation (3): ##EQU4## where i and j are item numbers attached to plant values, N is the number of samples of the residual used for calculation of the correlation function, and .phi..sub.ij is the correlation function with respect to the item number j of the item number i, which represents auto-correlation function when i=j and cross-correlation function when i.noteq.j.
By using the correlation function .phi..sub.ij obtained from the above-mentioned equation (3), a whiteness qualification index AL.sub.ij defined as the following equation (4) is obtained. ##EQU5## Then, by making use of the characteristic that AL.sub.ij depends upon the normal distribution N(0, 1) (having the average of 0 and the dispersion of 1), a threshold level is determined in accordance with the erroneous diagnostic level.
There was conducted a qualification such that when the following equation (5) holds, the correlation between the residuals .epsilon..sub.i and .epsilon..sub.j exists and this has no whiteness. EQU .vertline.AL.sub.ij .vertline.&gt;ARL (5)
In accordance with the above-mentioned diagnostic system, a typical abnormality or failure in the plants can be identified, but since information as to the time constant related to the dynamic characteristic of the plant is not included in the above equation (3) for calculating the correlation function .phi..sub.ij, an identification of abnormality or failure in consideration of the time constant of the plant to be diagnosed such that influence of the abnormality at a certain portion would be spread to another portion with a certain time delay could not be conducted.